If you're going to evaluate the intelligence of an animal, it's not enough to measure the size of its brain. Researchers are convinced that octopuses have an intelligence so sophisticated that they can display emotions and individual personalities. But it's a different sort of intelligence that has to be assessed in a different way:

Octopuses have the largest brains of any invertebrate. Athena's is the size of a walnut -- as big as the brain of the famous African gray parrot, Alex, who learned to use more than one hundred spoken words meaningfully. That's proportionally bigger than the brains of most of the largest dinosaurs.

Another measure of intelligence: you can count neurons. The common octopus has about 130 million of them in its brain. A human has 100 billion. But this is where things get weird. Three-fifths of an octopus's neurons are not in the brain; they're in its arms.

"It is as if each arm has a mind of its own," says Peter Godfrey-Smith, a diver, professor of philosophy at the Graduate Center of the City University of New York, and an admirer of octopuses. For example, researchers who cut off an octopus's arm (which the octopus can regrow) discovered that not only does the arm crawl away on its own, but if the arm meets a food item, it seizes it -- and tries to pass it to where the mouth would be if the arm were still connected to its body.

Intelligence is generally related to brain-body mass ratio. Bigger bodies require more neural mass to articulate them. An octopus has virtually no skeleton and it's limbs are muscular hydrostats - like the human tongue. The neural real estate needed to articulate a hydrostatic limb is quite a bit greater than that needed for a limb supported by bone. For example; the cortical homunculus depicts this fact in humans. The neural mass needed to support the tongue is close to the same amount needed to articulate the entire leg and foot.

Octopuses consist almost entirely of hydrostatic limbs and probably there are more sensory nerve fibres innervating the limbs as well. This means the octopus can have a disproportionate brain-body mass ratio compared to typical animals without being super intelligent in the sense of being able to write any Broadway musicals.

I would add that some human neurons are not in the brain either. In particular the lower motor neurons. The upper motor neurons originate in the sensory motor cortex of the brain. They course down the corticospinal tract - decussating at the medulla - and terminate in various parts of the spinal cord. If I remember correctly the arm UMNs terminate in the lower cervical spine (vertebrae C5-T1) of the spinal cord where they innervate Lower Motor Neurons (LMNs). It is these LMNs that actually articulate the limbs. So as in the octopus, our limb articulating neurons are not in our brains either. However the signal to articulate the limbs originates in the brain.